Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binarySearch(arr, l, r, x):   
    while l <= r: 
        mid = int(l + (r - l)/2); 
        if arr[mid] == x: 
            return True
        elif arr[mid] < x: 
            l = mid + 1
        else: 
            r = mid - 1
    return False


max = 100000 + 1
n = int(input())
array =  [0 for k in range(max)] 
array[0] = 0
found = False
for i  in range(1,max):
    array[i] = array[i-1]+i
for i in range(1,max):
    if(binarySearch(array,1,max,n-array[i])):
        print("YES")
        found = True
        break
if not found:
    print("NO")